use a formula sheet (i never got it) to help answer this:

sin(75degrees)

I suspect you need the sine of the sum of two angles, 45+30

Sin(A+B)=SinAcosB+cosAsinB

http://www.sosmath.com/trig/Trig5/trig5/trig5.html

I suspect you are suffering from lack of routine use of flash cards. Millions of students before you have suffered through memorizing these, as I did 55 years ago. Surely you can bear the pain.

I will make a guess at what is intended:

75 = 90 - 15
sin (a-b) = sin a cos b - cos a sin b
so
sin 90 cos 15 - cos 90 sin 15
= 1 cos 15 - 0 sin 15
= cos 15

15 = 30/2
cos a/2 = sqrt [(1+cos a)/2]
so
sqrt [ (1 + cos 30)/2 ]
but cos 30 = sqrt 3/2
so
sqrt [ (2+sqrt 3)/4 ]

To calculate the value of sine of 75 degrees, we can use the formula sheet that provides the values of trigonometric functions for common angles. However, if you don't have access to a formula sheet, there are still ways to find the answer.

One approach would be to use the angle addition formula for sine:

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

We can rearrange this formula to solve for sin(A). In this case, A will be our known angle of 75 degrees, and B will be a complementary angle such that A + B = 90 degrees.

Let's denote B as 90 - A. Therefore, B = 90 - 75 = 15 degrees.

Using the formula:

sin(75 degrees) = sin(75 degrees)cos(15 degrees) + cos(75 degrees)sin(15 degrees)

Now, we need to determine the values of sin(15 degrees) and cos(15 degrees), which we can obtain from either a calculator, a trigonometric table, or by using specific trigonometric identities.

If you have access to a calculator, you can enter sin(15) and cos(15) to get their approximate values, which are approximately 0.2588 and 0.9659 respectively.

Plug these values into the formula:

sin(75 degrees) ≈ sin(75 degrees) * 0.9659 + cos(75 degrees) * 0.2588

Calculating the expression:

sin(75 degrees) ≈ (0.9659 * sin(75 degrees)) + (0.2588 * cos(75 degrees))

Using a calculator to evaluate the trigonometric functions of 75 degrees:

sin(75 degrees) ≈ (0.9659 * 0.9659) + (0.2588 * 0.2588)

Performing the calculations:

sin(75 degrees) ≈ 0.9341 + 0.0671

sin(75 degrees) ≈ 1.0012

Therefore, sin(75 degrees) is approximately 1.0012.